I'm a strong supporter of using your conscience on the job, though you don't always get to. You don't always get to do what feels right because the boss disagrees, or the company policy is X, or it's someone else's job to make that decision.
I don't remember ever having to do something that felt very wrong. And I've never had to deny services to someone who was sorely in need.
Denying services is exactly what Kim Davis wants to do, so she doesn't get my support. If she feels that she can't issue marriage licenses, she can quit her job. If she doesn't want to quit her job (and that feeling is even stronger than her stance against same-sex marriage), she can tell herself that she isn't performing the weddings or even supporting them, she is only do the bureaucratic work of asking the state's questions, filling in answers, and determining whether applicants meet the state requirements.
However, Kim Davis doesn't have the power or mandate to decide who can get married and who can't. She wasn't elected to be the judge of those issues, so she very much oversteps her mandate when she refuses to issue marriage licenses. She ought to decide whether she is going to be a county clerk or going to be an conscientious Christian during her work hours. She wants to be both, but that isn't her remit. She should stop being a spoiled brat insisting on both, grow up, and make up her mind.
Extras. Town vs. college in Davis's hometown. Interesting political landscape. More quotes, but not more insight in this article.